Finite Group Databasebeta

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C4×#15688861 #26107160

order12032
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4×#15688861

Splittings

SylowC47 ⋊ C4×#328

Subgroups

subgroupG/H
centerC22×C4(C2×D47)⋊C4
commutatorC2×C4×C47C2×C42
FrattiniC23×C4C22×D47
FittingC4×C22⋊C8×C47C2
socleC23×C47C2×C22⋊C4
prime radicalC24×C47C2×D4
cosocleC23×C4×C47C23
hypercenterC4×C22⋊C8D47
hypocenterC47C4×#328
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×C22⋊C8

732 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1916 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 60450);